This paper uses panel data on household consumption and income to evaluate the degree of insurance to income shocks. Our aim is to describe the transmission of income inequality into consumption inequality. Our framework nests the special cases of self-insurance and the complete markets assumption. We assess the degree of insurance over and above self-insurance through savings by contrasting shifts in the cross-sectional distribution of income growth with shifts in the cross-sectional distribution of consumption growth, and analyzing the way these two measures of household welfare correlate over time. We combine panel data on income from the PSID with consumption data from repeated CEX cross-sections in a structural way, i.e. using conventional demand analysis rather than reduced form imputation procedures. Our results point to some partial insurance but reject the complete markets restriction. We find a greater degree of insurance for transitory shocks and differences in the degree of insurance over time and across education. We also document the importance of durables and of taxes and transfers as a means of insurance.